For one-dimensional fronts, we have found that the full dynamics of the discrete model defined in an Ising system based on the equilibrium model described in Ref. [1]} exhibits the same kinetic roughening behavior in terms of scaling exponents as the tensionless KPZ equation. To reach this result, we have represented the dynamics of the Ising system via a Ginzburg-Landau formulation which leads to an equivalent spin system. The interface thus defined has been shown to feature the same type of intrinsic anomalous scaling and the same exponent values as the tensionless KPZ equation. However, the PDF of the front fluctuations of the spin system (specially the tails, more influenced by boundary effects) does not fully reproduce the features of the PDF for the tensionless KPZ equation. Likewise, the latter does not
display multiscaling properties, in contrast with the fronts of the spin system. There are previous analogous cases in the literature in which discrete and continuum models in the same universality class do not behave equally with respect to e.g. the occurrence of anomalous scaling. For instance, for morphologically unstable diffusion-limited growth systems related with the paradigmatic diffusion-limited agregation (DLA) process [2]}, discrete models display intrinsic anomalous scaling [3]}, [4]}, while their continuum limits do not [5]}, [6]}. Likewise, under morphologically stable conditions, discrete models for the spreading of precursor
ultrathin films show anomalous scaling, not seen in continuum equations that provide the continuum limit [7]}. Hence, the discrepancy between the tensionless KPZ equation and our present results for 1D interfaces may be related with the fact that the latter have not yet reached their true scaling limit. In this way, much larger system sizes —at the corresponding higher computational cost— should be assessed in order to shed more light on the precise origin of these discrepancies.
